1. Field of the Invention
The present invention relates generally to variable impedances, and, in particular, to a variable impedance for use in a tank circuit.
2. Description of the Related Art
In general, in the descriptions that follow, I will italicize the first occurrence of each special term of art which should be familiar to those skilled in the art of radiofrequency (“RF”) communication systems. In addition, when I first introduce a term that I believe to be new or that I will use in a context that I believe to be new, I will bold the term and provide the definition that I intend to apply to that term. In addition, throughout this description, I will sometimes use the terms assert and negate when referring to the rendering of a signal, signal flag, status bit, or similar apparatus into its logically true or logically false state, respectively, and the term toggle to indicate the logical inversion of a signal from one logical state to the other. Alternatively, I may refer to the mutually exclusive boolean states as logic_0 and logic_1. Of course, as is well know, consistent system operation can be obtained by reversing the logic sense of all such signals, such that signals described herein as logically true become logically false and vice versa. Furthermore, it is of no relevance in such systems which specific voltage levels are selected to represent each of the logic states.
In general, in an RF communication system, an antenna structure is used to receive signals, the carrier frequencies (“fC”) of which may vary significantly from the natural resonant frequency (“fR”) of the antenna. It is well known that mismatch between fC and fR results in loss of transmitted power. In some applications, this may not be of particular concern, but, in others, such as in RF identification (“RFID”) applications, such losses are of critical concern. For example, in a passive RFID tag, a significant portion of received power is used to develop all of the operating power required by the tag's electrical circuits. In such an application, it is known to employ a variable impedance circuit to shift the fR of the tag's receiver so as to better match the fC of the transmitter of the system's RFID reader.
Although it would be highly desirable to have a single design that is useful in all systems, one very significant issue in this regard is the lack of international standards as to appropriate RFID system frequencies, and, to the extent there is any de facto standardization, the available frequency spectrum is quite broad: Low-Frequency (“LF”), including 125-134.2 kHz and 140-148.f kHz; High-Frequency (“HF”) at 13.56 MHz; and Ultra-High-Frequency (“UHF”) at 868-928 MHz. Compounding this problem is the fact that system manufacturers cannot agree on which specific fC is the best for specific uses, and, indeed, to prevent cross-talk, it is desirable to allow each system to distinguish itself from nearby systems by selecting different fC within a defined range.
As explained in, for example, U.S. Pat. No. 7,055,754 (incorporated herein by reference), attempts have been made to improve the ability of the tag's antenna to compensate for system variables, such as the materials used to manufacture the tag. However, such structural improvements, while valuable, do not solve the basic need for a variable impedance circuit having a relatively broad tuning range.
Shown in FIG. 1 is an ideal variable impedance circuit 2 comprised of a variable inductor 4 and a variable capacitor 6 coupled in parallel with respect to nodes 8 and 10. In such a system, the undamped resonance or resonant frequency of circuit 2 is:
                              ω          R                =                  1                      LC                                              [                  Eq          .                                          ⁢          1                ]            
where:                wR=the resonant frequency in radians per second;        L=the inductance of inductor 2, measured in henries; and        C=the capacitance of capacitor 6, measured in farads.        
On, in the alternative form:
                              f          R                =                                            ω              R                                      2              ⁢                                                          ⁢              π                                =                      1                          2              ⁢                                                          ⁢              π              ⁢                              LC                                                                        [                  Eq          .                                          ⁢          2                ]            
where:                fR=the resonant frequency in hertz.        
As is well known, the total impedance of circuit 2 is:
                    Z        =                  RLS                                    RLCS              2                        +            LS            +            R                                              [                  Eq          .                                          ⁢          3                ]            
where:                Z=the total impedance of circuit 2, measured in ohms;        R=the total resistance of circuit 2, including any parasitic resistance(s), measured in ohms;        L=the inductance of inductor 2, measured in henries; and        S=jω;        where:                    j=the imaginary unit √{square root over (−1;)} and            ω is the resonant frequency in radians-per-second.                        
As is known, for each of the elements of circuit 2, the relationship between impedance, resistance and reactance is:Ze=Re+jXe  [Eq. 4]
where:                Ze=impedance of the element, measured in ohms;        Re=resistance of the element, measured in ohms;        j=the imaginary unit √{square root over (−1;)} and        Xe=reactance of the element, measured in ohms.        
Although in some situations phase shift may be relevant, in general, it is sufficient to consider just the magnitude of the impedance:|Z|=√{square root over (R2+X2)}  [Eq. 5]
For a purely inductive or capacitive element, the magnitude of the impedance simplifies to just the respective reactances. Thus, for inductor 4, the magnitude of the reactance can be expressed as:XL=|j2πfL|=j2πfL  [Eq. 6]
Similarly, for capacitor 6, the magnitude of the reactance can be expressed as:
                              X          C                =                                                        1                              j                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                fC                                                          =                      1                          2              ⁢                                                          ⁢              π              ⁢                                                          ⁢              fC                                                          [                  Eq          .                                          ⁢          7                ]            
Because the reactance of inductor 4 is in phase while the reactance of capacitor 6 is in quadrature, the reactance of inductor 4 is positive while the reactance of capacitor 6 is negative. Resonance occurs when the absolute values of the reactances of inductor 4 and capacitor 6 are equal, at which point the reactive impedance of circuit 2 becomes zero, leaving only a resistive load.
As is known, the response of circuit 2 to a received signal can be expressed as a transfer function of the form:
                              H          ⁡                      (                          j              ⁢                                                          ⁢              ω                        )                          =                                            1              R                        +                          j              ⁡                              (                                                                            -                      C                                        ⁢                                                                                  ⁢                    ω                                    +                                      1                                          L                      ⁢                                                                                          ⁢                      ω                                                                      )                                                                        1                              R                2                                      +                                          (                                                                            -                      C                                        ⁢                                                                                  ⁢                    ω                                    +                                      1                                          L                      ⁢                                                                                          ⁢                      ω                                                                      )                            2                                                          [                  Eq          .                                          ⁢          8                ]            
Within known limits, changes can be made in the relative values of inductor 4 and capacitor 6 to converge the resonant frequency, fR, of circuit 2 to the carrier frequency, fC, of a received signal. As a result of each such change, the response of circuit 2 will get stronger. In contrast, each change that results in divergence will weaken the response of circuit 2.
A discussion of these and related issues can be found in the Masters Thesis of T. A. Scharfeld, entitled “An Analysis of the Fundamental Constraints on Low Cost Passive Radio-Frequency Identification System Design”, Massachusetts Institute of Technology (Aug. 2001), a copy of which is submitted herewith and incorporated herein in its entirety by reference.
I submit that what is needed is an efficient method and apparatus for dynamically varying the impedance of a tank circuit, and, in particular, wherein the impedance of the circuit can be efficiently varied so as to dynamically shift the fR of the circuit to better match the fC of a received signal and thereby improve the response of the circuit.